Complex Impedance of Fast Optical Transition Edge Sensors up to 30 MHz

Abstract

Optical transition edge sensors (TESs) are characterized by a very fast response, of the order of $\upmu$s, which is $10^3$ times faster than TESs for X-ray and gamma-ray. To extract important parameters associated with the optical TES, complex impedances at high frequencies (> 1 MHz) need to be measured, where the parasitic impedance in the circuit and reflections of electrical signals due to discontinuities in the characteristic impedance of the readout circuits become significant. This prevents the measurements of the current sensitivity $\beta$, which can be extracted from the complex impedance. In usual setups, it is hard to build a circuit model taking into account the parasitic impedances and reflections. In this study, we present an alternative method to estimate a transfer function without investigating the details of the entire circuit. Based on this method, the complex impedance up to 30 MHz was measured. The parameters were extracted from the impedance and were compared with other measurements. Using these parameters, we calculated the theoretical limit on an energy resolution and compared it with the measured energy resolution. In this paper, the reasons for the deviation of the measured value from theoretically predicted values will be discussed.